For the mechanism `A+B ? K_(2) C, C overset(k_(3)) rarr D`
(a) Derive the rate law using the steady-state approximation to eliminate the concentration of C.
(b)\ Assuming that `k_(3) lt lt k_(2)`, express the pre- exponential factor A and `E_(a)` for the apparent second- order rate constant in terms of `A_(1), A_(2) and A_(3) and E_(a1), E_(a2) and E_(a3)` for the three steps.

Explanation

To solve the problem step by step, we will derive the rate law using the steady-state approximation and then express the pre-exponential factor and activation energy for the apparent second-order rate constant.

### Step-by-Step Solution

**(a) Deriving the Rate Law using the Steady-State Approximation:**

1. **Write the Mechanism:**
The given mechanism is:
...